Choi matrices revisited. II
Quantum Physics
2023-10-13 v3 Operator Algebras
Abstract
In this paper, we consider all possible variants of Choi matrices of linear maps, and show that they are determined by non-degenerate bilinear forms on the domain space. We will do this in the setting of finite dimensional vector spaces. In case of matrix algebras, we characterize all variants of Choi matrices which retain the usual correspondences between -superpositivity and Schmidt number as well as -positivity and -block-positivity. We also compare de Pillis' definition [Pacific J. Math. 23 (1967), 129--137] and Choi's definition [Linear Alg. Appl. 10 (1975), 285--290], which arise from different bilinear forms.
Cite
@article{arxiv.2307.09247,
title = {Choi matrices revisited. II},
author = {Kyung Hoon Han and Seung-Hyeok Kye},
journal= {arXiv preprint arXiv:2307.09247},
year = {2023}
}
Comments
17 pages; the comma in the title has been replaced to a period; to appear in Journal of Mathematical Physics